1. Are we, as some might say, motivated by a desire to save our off-spring?
Yes because as our off-spring grows up, we form not only biological bonds but psychological bonds as well. To think on an extreme level, some people think their offspring as a very prized possession. If someone was trying to steal or destroy your Portable Playstation, would you not save it?

2. Must there always be some sort of intrinsic reward for doing good?
Not all the time but for most of the time, yes. The way society has shaped young adults these days has made them greedy. You could even say that technology made them into greedy little high school students.

3. Mr. Otis once said, "That having integrity is doing the right thing when no one is watching." If this is so, and no one knows when we have done good, would you still do good?
For me, I would keep it in mind but it would not be one of my top priorities. However, in general, I do not think that most people would do it because of the demands of the students. Most students these days are greedy and in order to make them motivated, there must be a prize or a reward.

4. "Delayed reciprocal altruism", seems like a gamble - back to game theory, any way. Does this seem to make sense to you. That is that we act out of a desire to have what we have done being done to us?
I believe that when a person helps a person on purpose, it is because they have the desire to have what they had done being done to them. However, when one is sub-consciously helping people, it is more of an instinct than a purpose.

5. Are we ever being truly "selfless" when committing an act of altruism?
There is the rare occasion where one might abandon himself in order for the happiness of others. However, this may come only in fairy tales. In modern times, people only do selfless things when they are ordered to.